Critical Points Practice

Identify the critical points of the following function:
g(x)=2x³-3x²

• x=-1,1
• x=0,0
• x=0,-1
• x=0,1

What is the relative maximum value?

• y = 4
• y = 2
• y = 1
• y = -1

Given a function g(x), if g'(x)=0 at a certain value of x, then g(x) has _____________ at x.

• an inflection point
• a critical point
• a minimum
• a maximum

Find the derivative of the given equation
f(x) = x³ + x² + 3

• 3x² + 2x
• 3x + 2x 
• 3x + 2x + 3
• x³ + x² 

When f'(x) changes from negative to positive, there is(are) ...

• a maximum.
• a minimum.
• no extrema.

Find all the critical numbers of

f(x) = 2x³ – 6x² + 12

Select ALL that apply.

• x= 4

• x= 0

• x= -2

• x= 2

Find the critical number of f(x) = 4x² – 8x + 1

• x = 2

• x = 0

• x = 8

• x = 1

• x=2

• x=0

• x= -4

• x= -2

• x = 4

If a function's FIRST derivative is negative at a certain point, what does that tell you?

• The function is increasing at that point
• The function is decreasing at that point
• The concavity of the function is up at that point
• The concavity of the function is down at that point

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression